Incorrect second order Lagrange Hexahedral order
Hi. In Release notes on higher order Lagrangian cells, there is an image illustrating the ordering of a Lagrange order 3 hexahedron element. The number of the hexahedron element does not correspond to the ordering used for Lagrange order 2 hexahedron elements. I've attached an example where the points are ordered as one would expect by looking at the Lagrange order 3 example:
<!-- <DataArray type="UInt32" Name="connectivity" format="ascii">0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 </DataArray> -->
- Vertices at z=0 counter clockwise
- Vertices at z=1 counter clockwise
- Edges at z=0 counter clockwise (starting with the one between vertex 0 and 1)
- Edges at z=1 counter clockwise (starting with the one between vertex 4 and 5)
- Edges at z=0.5 counter clockwise
- Faces, since we are considering CG2 there is only one dof per faces. Describing them with planes: (XZ, Y=0), (XZ, Y=1), (YZ, X=0), (YZ, X=1), (XY, Z=0), (XY, Z=1)
- One internal node.
This ordering does not yield the correct connectivity visually.
The correct ordering would be:
<!-- <DataArray type="UInt32" Name="connectivity" format="ascii">0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 </DataArray> -->
This implies that step 5 is wrong. This should be a lexicographical ordering.
Similarly, step 6 is wrong.
I've attached a mesh with the ordering that's working visually in Paraview 5.7.0-RC4.
CG2_hex.pvd